"Our greatest responsibility is to be good ancestors."

-Jonas Salk

Saturday, June 18, 2011

Sustained Growth is Impossible

In the long run, all real-world growth rates asymptote to zero.

It seems to me that there are two kinds of people; those who understand this as a crucial basis for reasoning about the world, and those who don't.

If you're in the latter category, this may help. It's a very accessible introduction to exponential growth, featuring Prof A. Bartlett of Colorado:

(multipart video continues here)

The way to duck this distinction is to say you don't care about the very long run. Maybe the story about somebody speaking for the seventh generation in tribal meetings somewhere is true and maybe it isn't. But as we become more and more a force of nature, our behavior impacts even the seventieth generation. To make our time horizons shorter and shorter as our impacts get longer and longer is obviously flatly unethical, though not entirely irrational.

But for those who don't understand the argument (rather than choosing to duck it) there are a couple of places to look.

Joel Cohen in his nonfiction magnum opus "How Many People Can the Earth Support?" makes the case well. I was surprised to see a comparable argument on a business site. Henry Blodget quotes Jeremy Grantham to make the case on Business Insider.


Steve Bloom said...

This makes me wonder if science fiction, of which I'm a life-long fan, hasn't done rather a lot of damage by promoting the idea of what I suppose we could call resource utopias.

William M. Connolley said...

Its pretty irritating to be pointed at a youtube video. Do you have a text version? Then I'd know exactly what kind of things you have in mind whose sustained growth is impossible. For an obvious counter-example, the growth in f(t) = exp(t) doesn't asymptote to zero.

Steve Bloom said...

Just to note the absolutely pernicious confluence of the foregoing with American exceptionalism.

Steve Bloom said...

Er, not Stoaty, the one before, although pernicious would hardly do justice to a combination of him with American exceptionalism. :)

Michael Tobis said...

William, good points. Fixed on both accounts.

King of the Road said...


In the real world growth only follows f(t)=k*exp(t) for a finite period. I think a better function for our growth is more like:


I sure wish I could insert Latex in a comment. But here, (1/N)*diff(N,t) is the specific growth rate (with N as population and t as time). a0 is your "k" in the equation above, b is a "crowding coefficient," related to carrying capacity, and the integral is the accumulated "self-poisoning" in its most general sense, i.e., air and water pollution, desertification, ozone destruction, warming, sea level rise, extinctions of food supply, etc. etc. etc.). This equation not only doesn't asymptote to zero for a growth rate, it goes to zero for population.

I would regard this as unfortunate.

Moth said...

A while ago, my boss gave me a VHS of Prof. Bartlett to convert to an .avi file, as I had the tech on my personal computer.

It's an excellent presentation - it's looks to be the same as this one. I'm not sure if I'm allowed to distribute it however (thought on many times that I should put it on youtube).

Anonymous said...

This is an excellent presentation from professor Bartlett.

There's a torrent of Arithmetic, Population and Energy, but I think it differs slightly from the Youtube video.

Here are Bartlett's Laws of Sustainability.

Michael Tobis said...

Neven, the Laws of SUstainability is an astonishingly valuable piece, seriously one of the best things I have seen on the internet.


Rich Puchalsky said...

Not very impressed with "the laws of sustainability". Statements like:

"Fifth Law: One cannot sustain a world in which some regions have high standards of living while others have low standards of living."

pretty much equate to

"There is no such thing as culture."

Adam said...

Steve Bloom said...
This makes me wonder if science fiction, of which I'm a life-long fan, hasn't done rather a lot of damage by promoting the idea of what I suppose we could call resource utopias.

Recall the replicators on Star Trek: anything one desired, on command.

Where did the replicators get their "stuff"? Were Federation star ships like galactic whale sharks, sifting the necessary materials from interstellar detritus?

Did Federation troopers get paid? If so, what did they spend it on? Replicator credits? How much did a a cup of "...tea, Earl Gray, hot" cost? One Standard Value Unit (SVU)?

--Adam R.

Michael Tobis said...

I've avoided the "why space won't save the earth" rant so far but it will have to come out someday...

Michael Tobis said...

Rich, you'll have to elaborate; I don't see your point.

Rich Puchalsky said...

All right, I'll elaborate. It is perfectly sustainable to have a world where some areas have high standards of living while others have low standards of living. Here are a few possible cases:

1. The low standard of living area has a culture in which a high standard of living is not valued, for whatever religious or political reasons.

2. The low standard of living area has a culture in which people are not educated, and therefore are outcompeted for resources by higher standard of living areas.

3. The low standard of living area is kept that way by a dictatorship (of whatever type) that finds people easier to control that way.

Assuming that everyone wants a First World standard of living and will inevitably proceed there if not stopped by resource constraints is just cultural imperialism. It's the flip side of the same unthinking "our way is obviously better and everyone wants to be like us" that encourages us to try to export our culture to everyone and try to make it a self-fulfilling prophecy.

If, for instance, people take up the project that you're advocating on giving up on growth, some people are going to take it up before others. Unless it occurs due to a world-wide crash, there are some areas that are going to have a "low standard of living" because they choose to. Of course this gets into definitional questions of what makes a low standard of living -- access to free, high-quality medical care, or access to a car? But those definitional questions are themselves cultural.

In short this sustainability list smells like the U.S. 1970s. It doesn't even mention women's rights, the largest single factor in limiting population growth. You might want to look up what happened to the Sierra Club in 2004. (Here to start.) Clueless buy-in to right-wing tropes doesn't help.

Michael Tobis said...

I get the feeling everything you don't like becomes a "right wing trope".

Yes, of course in principle a society could choose to give up its share.

In practice I don't know of any society (as opposed to a sect or a self-selected group of some kind) that does not aspire to at least the contemporary global mean footprint, which already butts up against sustainability issues.

I think Bartlett is trying to say that if the higher footprint society endeavors to enforce that difference on the lower footprint society it's unsustainable.

Yes, if the population ever becomes small enough, societies may voluntarily reduce their footprints below the much laxer constraints. But foreseeably, international equity is a key problem.

More germane is the question of whether a scenario of perpetual global inequity enforced by a wealthy subgroup is sustainable.

That is something one might argue, but it is clearly corrupt and undesirable. I think this is one of the dystopias we need to avoid. And it's hard to imagine it working out indefinitely.

Michael Tobis said...

Sustainability is a meaningless concept in a national context.

There is no immediate prospect for substantial immigration on to or off of the planet. Sustainability is a condition to be achieved or not achieved by the entire planet.

Immigration issues do tie into the international equity issues of course. But whatever motivations go into either side of those debates in particular nations are irrelevant to the global aggregate.

There is nothing particularly 1970's about thinking in terms of the global aggregate.

Rich Puchalsky said...

Good luck talking to or thinking for the global aggregate.

"And it's hard to imagine it working out indefinitely."

Do you really think that anyone has a chance of finding an indefinite solution to anything? That implies changelessness. And it's reminiscent of the vanity of the people who want to find a permanent solution to the deficit (let's say) in the U.S. How are they going to bind some future set of legislators from changing their plans?

International equity is of course important. But national and cultural differences exist and will continue to exist. If we're going to progress towards sustainability in our time, it's going to be a sustainability that takes different forms in different places.

Michael Tobis said...

It's interesting you should say this. I am increasingly of the opinion that only an international political movement will suffice to achieve what we need.

Copenhagen made it clear that the existing sovereignties do not have the power to act adequately on behalf of later generations.

What would suffice is an agreement binding on everybody that achieves the necessary goals in the aggregate. But they cannot do it because everybody reports to an authority smaller than the totality, and nobody speaks for the earth.

"Do you really think that anyone has a chance of finding an indefinite solution to anything?"

I see no alternative whatsoever to universal respect for the law of the asymptote. The average growth rate of any quantity over a long enough time is zero. Period. Any policy which ignores this eventually leads to problems. Period.

Nature always bats last. One way for Nature to arrive at a zero growth quantity is to have zero of that quantity.

I would like us to stick around. If we want to stick around, we have to obey the rules of the universe, not of this or that culture. If that is insurmountable, we are out of here.

I think this has to come from a populace that sufficiently understands the risks that most are starting to feel. From that understanding may come enough pressure to act. If we leave it to the increasingly incompetent domain of partisan quibbling we stand no chance of being good ancestors.

One more absolute feature of sustainability is that every culture on earth understands and adapts to the constraints of sustainability, forever.

Tall order? Indeed it is.

In one of his shiny moments, Revkin compared it to the onset of the adult phase of a sentient species. Late adolescence is a difficult time; not everyone succeeds in growing up.

Dol said...

On the fifth law: think I agree with Rich on the basic point. To say that equality is a natural-law-like outcome of achieveing sustainability is just wrong. It might be a normative goal, an ethical imperative for some, but raising it to a law?

The `law' of factor equalisation should in theory do away with differences in wages... that is, until Krugman comes along and finds some different mathematical idea able to `explain' economically the emergence of core and periphery.

I think it's very important to be clear on this: there is a version of the future which is a) sustainable and b) massively hierarchical economically. E.g. in a sustainable world with rich car-owners and poor people requiring land for food, car-food will make people-food harder to come by. (Happening now of course. Assume 'car-owners' are possible, it's only a thought experiment.)

If we want to try and build an equitable world, OK. If we want to work towards a future that's both equitable AND sustainable, also OK: there are specific arguments to be made, specific paths that make both more likely together. BUT: I think it's dangerous to argue that a sustainable future MUST be equitable as a necessity.

Arnaud said...

Michael, as one space cadet which (with many others) see on the contrary that space -could- save the Earth (which doesn't mean it -will- of course), I would be highly interested indeed to hear your arguments. When can we expect a piece on this?

Rich Puchalsky said...

And I agree with Dan Olner. Remember this cartoon posted over at Stoat? It's the one where (among other things) the environmentalists on the sinking ship are saying "the solution must be green." It plays into the sentiment, which I've seen expressed here too, that people who are too picky about solutions are part of the problem. Yet you're going to insist that a solution in which some areas are high standard of living while others are lower is not sustainable?

And whether you realize it or not, this:

"One more absolute feature of sustainability is that every culture on earth understands and adapts to the constraints of sustainability, forever."

is a recipe for genocide.

Of course there are going to be cultures that are actively committed to growth -- to having many children, say. Or religious minorities within cultures. If you imagine that everyone else takes your dictat seriously, the only solution is to kill them.

In fact, the time-honored solution is to recruit their children. The core of the culture goes on, and most of their children are enticed by the higher standrd of living in less crowded or more educated places elsewhere. Sustainability as a whole is preserved with a group of people committed to growth who end up being a feeder society for a larger group of people with a slightly lower than replacement level of growth.

But without honoring differences like this as long as the overall system works out OK, you're advocating something that's really very bad, politically. It's clueless at best, and people who are not used to thinking of themselves as the global model for the standard citizen quickly see that.

Shining Raven said...

@Arnaud: Try Charles Stross on space colonization:



and especially for you as a self-proclaimed "space cadet":



Dol said...

"... is a recipe for genocide."

A bit strong! There is a bit of a confusion in the line you're quoting though. All cultures are ultimately embedded in ecosystems. I think the quote is taking that positive statement and trying to make it normative, which is just a mixing up of is/ought.

You've gone too far with the genocide claim: cultures exist / have existed that *have* adapted to a sustainable way of life (in the sense that they've managed to work out how to exploit their environment indefinitely.) I just doubt that their existence can be raised to the level of a principle.

Makes me think of the (original) colonisation of the Americas: massive ecological collapse, the end of all the megafauna, and eventually a small subset of people who managed to stumble across ways to survive - presumably through sheer trial and error...

We presumably want to avoid that sort of outcome. Doubtless some people will survive, but it'd be nice if we could have a little more foresight and pre-empt a complete collapse. The signs are not looking good.

Rich Puchalsky said...

"Makes me think of the (original) colonisation of the Americas: massive ecological collapse, the end of all the megafauna, and eventually a small subset of people who managed to stumble across ways to survive - presumably through sheer trial and error... "

And all the other societies die off. In a situation like ours, in which the primary competition is intra-species, that means genocide.

I'm not saying that it isn't possible for a hunter-gatherer culture to achieve sustainability. Most of them do. But if you claim to be thinking at a global level, as MT is, and you believe that all cultures must accept X (where X is almost anything), then you are setting yourself up with reasons for genocide. Cultures that don't want to give up on growth aren't just going to starve when things go bad. They're going to use force. If you can't have a system that they are a part of, you're basically claiming that you're going to have to kill them.

If you want to think of it a different way, consider the following:

"Fifth Law: One cannot sustain an ecosystem in which some animals have high standards of living while others have low standards of living."

It's just this left-over nonsense from the 1970s in which everyone was supposed to inevitably become part of the same culture, the universal master culture which just so happened to be the culture of the U.S. middle class.

Rich Puchalsky said...

Here's a case study: are the Amish sustainable?

Wiki says that they have 200,000 or so population -- about 1/10th of the U.S. prison population. They are one of the fastest growing populations in the world. They are opposed to birth control, and it seems unlikely that they could be convinced to reduce their family sizes.

Their standard of living is unquestionably lower than that of the surrounding areas, by any of the standard measures. By the same token, I'd guess that their per-person environmental impact is much lower -- they don't drive, use the electrical net, etc.

I don't see any reason why a world with them in it isn't sustainable, even if they never agree to respect MT's universal demand. As their community grows, there is unavoidably more contact with people outside, and they lose some youngsters to the lifestyle of the surrounding area. Their own high family sizes are balanced out by their low per-person impact. Over a long period of time, all else being stable, you might expect to see a lot of people whose ancestors were Amish at one point but who themselves are not, and the Amish population overall to stabilize at the point at which loss of children to other cultures balances growth. That's inescapably a political/cultural matter, not a resource-driven one, and can't be expected to be a constant for forever.

They are an easy case for dismissal because they are relatively small and have no political power. But the more you try to universalize laws that aren't laws, the more people you need to sweep under the rug.

SteveH said...

Name one non-renewable resource that we have run out of. The one resource that is without limits is the human imagination. If you are peddling sustainability you have run out of ideas. These notions of sustainability always have elaborate technical or engineering solutions that inevitability devolve to rule by experts.

Michael Tobis said...


susan said...

Food for thought, thanks.

Circumstances have forced me to think about how many people think they are superior to other people. The point I take (and agree with) from the standard of living issue is that ethically we cannot hoard our comforts and say others are not entitled to them. This means we can't make a plan that involves building a moat around our possessions in the old-fashioned way. Nature doesn't accept those kinds of walls for long.

Meanwhile, people are having babies the way they always have, without regard for what they know or don't know about the future. This is normal, and asking people not to be normal is a very long shot.

Hoarding as a coping mechanism bears a strong resemblance to putting quarterly profits in front of long-term development.

I also agree that sustainability has become a kind of feel-good mantra. But what to do?

One other cruel consequences is the increasing prevalence of wars over scarce resources (water, oil).

Dol said...

Reading something I wrote on Bartlett a coupla years back, it turned out he actually thinks education is in the 'makes the problem worse' column. Just checked - part 2, around 7.45 in.

It's a throwaway line: he's thinking only of the fact that people haven't been educated about limits to growth, I think, and so don't understand the problem.

Repeating myself now, but it does make me think about other seemingly a priori ways of thinking about the problem e.g. reducing all energy analysis to talk of the 2nd law. As with Prof Bartlett, though, it's something physicists seem to love having a go at.

Jim Bouldin said...

"Name one non-renewable resource that we have run out of. The one resource that is without limits is the human imagination."

Aside from the direct contradiction that statement represents, many people these days cannot distinguish imagination from fabrication. They really can't.